1Modeling arrival process
22-05-2012
Challenge the future
DelftUniversity ofTechnology
Modeling the arrival process at dry bulk terminalsDelft University of Technology
T.A. van Vianen, J.A. Ottjes and G. LodewijksFaculty 3ME, Transport Engineering & Logistics
2Modeling arrival process
Content
• Arrival process• Average port time• Modeling arrival process• Continuous quay layout or multiple berths• Conclusions
3Modeling arrival process
Arrival process (1)• Typical performance indicator is the average ships’
waiting time• Agreements between terminal operators and ship-owners
are made about the maximum ships’ port time• Demurrage costs have to be paid if ships stay longer in
the port• How much capacity must be installed at the quay side?
Ship unloading (Courtesy of J.Hiltermann)Ship loading (Courtesy of Richards Bay Coal Terminal)
4Modeling arrival process
Arrival process (2)• How to prevent that ships are queuing before getting
serviced?
Ships waiting before servicing
Quay side capacity
Cost
s
Demurrage costs
Operational costs
Find the optimum
5Modeling arrival process
Content
• Arrival process• Average port time• Modeling arrival process• Continuous quay layout or multiple berths• Conclusions
6Modeling arrival process
Average port time (1)• Average port time is the average waiting time plus the
average service time• Ships’ interarrival time predominately determines the
average waiting time• Quay crane capacity and carriers’ tonnage determines
the average service time
Carrier tonnage distribution
Nr. of berths
Crane capacityNr. of cranes
Anchorage position
Arrival process
Waiting
Servicing
7Modeling arrival process
Average port time (2)• Existing literature about ships’ arrivals:
• Ships do not generally arrive at their scheduled times because of bad weather conditions, swells and other natural phenomena during the sea journey as well as unexpected failures or stoppages (Jagerman and Altiok, 2003)
• Uncontrolled ship arrivals results in ship delays (Asperen, 2004)• Ships interarrival times best approximated by a Poisson or
Erlang-2 arrival process (UNCTAD, 1985)• An Erlang-2 distribution can be used to represent the service
time distribution (UNCTAD, 1985 and Jagerman and Altiok, 2003)
8Modeling arrival process
Average port time (3)• But what is meant with Poisson or Erlang-2 distributed
interarrival times?• In a Poisson and Erlang-2 arrival process, probability
distributions express the probability of a ship arrival in a fixed interval of time
0
0.02
0.04
0.06
0.08
0.1
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
Freq
uenc
y [-
]
Ships' interarrival time [h]
Poisson
Erlang-2
Poisson and Erlang-2 distributions for ships’ interarrival times with an average of 10 hours
9Modeling arrival process
Average port time (4)• From 3 terminals, the arrival process was investigated to
check real-world data with existing literature• T1: single-user, import terminal
• T2: stevedore, import terminal
• T3: single-user, export terminal
Interarrival time distributions
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
105
110
115
120
125
130
135
140
145
150
155
160
Freq
uenc
y [-
]
Interarrival time [h]
T1 - 345 arrivals - 2.25 yearsT2 - 898 arrivals - 3 yearsT3 - 186 arrivals - 1 year
T1 ~ Erlang-2T2 PoissonT3 ~ Normal
Interarrival time distribution depends on terminal type
10Modeling arrival process
Average port time (5)• Service time relates directly to the carriers’ tonnage
Carriers’ tonnage distributions
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
5 15 25 35 45 55 65 75 85 95 105
115
125
135
145
155
165
175
185
195
205
215
225
235
245
255
265
275
285
295
305
315
Freq
uenc
y [-
]
Carriers' tonnage [kt]
T1 - 345 arrivals - 2.25 yearsT2 - 898 arrivals - 3 yearsT3 - 186 arrivals - 1 year
Real-world data does not correspond with the suggested Erlang-2 distribution
11Modeling arrival process
Content
• Arrival process• Average port time• Modeling arrival process• Continuous quay layout or multiple berths• Conclusions
12Modeling arrival process
Modeling arrival process (1)• Modeling of the arrival process based on Queuing Theory
Basic of a queuing system
Queuing system
Service facility
Queue
-/-/-
Interarrival times distribution
Service times distribution
Number of servers
Labeling of queuing models
• M/E2/2:• Interarrival times distributed according a Poisson
(Markovian) arrival process• Service times distributed according Erlang-2 distribution• 2 servers 2 berths where each berth is equipped with 1
quay crane
13Modeling arrival process
Modeling arrival process (2)• For single berth queuing systems, the impact of the
several interarrival times distribution was investigated
Average waiting time, expressed in average service time, versus quay occupancy for single berths
0
0.5
1
1.5
2
2.5
3
3.5
4
0.3 0.4 0.5 0.6 0.7 0.8 0.9
Wt [
1/μ]
ρ (λ/μ) [-]
M/E2/1E2/E2/1D/E2/1
D/E2/1:
Anchorage position
Single berth queuing system
134 1tW
112 1tW
114 1tW
M/E2/1:
E2/E2/1:
14Modeling arrival process
Modeling arrival process (3)• For multiple berths queuing systems, there are hardly
mathematical expressions
M/M/s:
Anchorage position
Multiple berths queuing system
1
1
,1
sC
sWt
E2/E2/s: ……..
Graphs of UNCTAD can be used, but what if the service time cannot be represented with an analytical distribution?
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
unlo
adin
g ca
paci
ty p
er h
our
[%]
unloading time [%]
50% of load 35% of load 15% of load
Research had shown that the unloading capacity is not constant during the entire ship unloading
15Modeling arrival process
Modeling arrival process (4)• A discrete-event simulation model was developed
ShipGenerator
ShipQ
QC1
QC2
QCn
Terminal quay
Ship
Simulation model
Classes with attributes
Distribution Types Options
Ship
MyTonnage
Quay Crane (QC)
MyShip
Capacity
ShipGenerator
MyShipIATDist. Type
TonnageDist. Type
ProcessProcess
IATDist. Type:
Poisson
Erlang-2Deterministic
ShipFile
TonnageDist. Type:
Erlang-2
DeterministicTableDistribution
ShipFile
CraneClass.ProcessMyDistGen.Start(Tnow)While True doBegin
If IsInQueue(CraneIdleQ) then MyDistGen.PauseWhile IsInQueue(CraneIdleQ) do standby; If MyDistGen.Status = interrupted then MyDistGen.Resume(Tnow);If MyShip <>nil thenBegin
if MyShip.Tons > 0 then Begin MyShip.Tons:=MyShip.Tons – GrabTons; Hold(Cranecycle);end;if MyShip.Tons = 0 thenBegin If (IsInQueue(MyBerth.MyCranesQ)) and
(MyBerth.MyCranesQ.Length > 1) then Begin LeaveQueue(MyBerth.MyCranesQ); LeaveQueue(CraneActiveQ); End; if (IsInQueue(MyBerth.MyCranesQ)) and
(MyBerth.MyCranesQ.Length = 1) then Begin LeaveQueue(MyBerth.MyCranesQ); LeaveQueue(CraneActiveQ); MyBerth.MyShip.Destroy; MyBerth.LeaveQueue(BerthOccupiedQ); MyBerth.EnterQueue(DeberthQ); end; EnterQueue(CraneIdleQ);end;
end;End;
16Modeling arrival process
Modeling arrival process (5)• For multiple berths queuing systems, the simulation model
was used to determine the average ships’ waiting time
17Modeling arrival process
Modeling arrival process (6)• For multiple berths queuing systems, the simulation model
was used to determine the average ships’ waiting time
(M/E2/1: 1.75, M/E2/2: 0.75, M/E2/3: 0.58, M/E2/4:
0.28)
0
0.5
1
1.5
2
2.5
3
3.5
4
0.3 0.4 0.5 0.6 0.7 0.8 0.9
Wt [
1/μ]
ρ (λ/sμ) [-]
M/E2/1M/E2/2M/E2/3M/E2/4
Average waiting time, expressed in average service time, versus quay occupancy for multiple berths
Anchorage position
Multiple berths queuing system
18Modeling arrival process
Modeling arrival process (7)• Can analytical models be used for an accurate arrival process modeling?• The simulation model was used to compare terminals’ real-world arrival data with
analytical models
Tonnage minimum [t]
Tonnage maximum [t]
[%]
0 25,000 5* 25,000 50,000 19.4 50,000 75,000 23.6 75,000 100,000 10.1
100,000 150,000 12.3 150,000 200,000 25.5 200,000 300,000 4.1
* 5% of all bulk carriers were generated with tonnages between 0 tons and 25,000 tons.
Table distribution to represent carriers’ tonnage for T2
Comparison real-world data with analytical models
19Modeling arrival process
Content
• Arrival process• Average port time• Modeling arrival process• Continuous quay layout or multiple berths• Conclusions
20Modeling arrival process
Continuous quay layout or multiple berths (1)
A) Continuous quay layoutB) Multiple berths
operation
Interarrival time distribution type NEDBulk carriers tonnage distribution Table Input Number of quay cranes [-] 4Max. number of ships at the quay [-] 4
Quay crane capacity (free-digging) 3,000 [t/h]
Annual throughput [Mt] 20 – 50Runtime of simulation [years] 5Simulation input
(A)
BC1 BC2 BC3
(B)
BC1 BC2 BC3
Berth 1 Berth 2 Berth 3 Berth 4
C1 C2 C4C3 C4’
C1 C2 C3 C4
21Modeling arrival process
Continuous quay layout or multiple berths (2)
Occupied quay length versus annual throughput
600
700
800
900
1,000
1,100
1,200
1,300
20 25 30 35 40 45 50
Qua
y le
ngth
[m]
Annual Throughput [Mt]
M/G/4M/G/4+ [2]M/G/4+ [3]M/G/4+ [4]
22Modeling arrival process
Conclusions• Serving ships on time and at correct speed is crucial for terminal operators• Modeling the ships’ arrival process is required to design the terminal’s quay side• The ‘wilder’ the arrival pattern, the greater the average waiting time• Modeling the arrival process must be based on Queuing Theory• However, for multiple berths there are hardly analytical solutions and a discrete-event simulation is proposed• For an accurate modeling, it is proposed to use a table distribution which represents the carriers’ tonnage instead of using analytical models for the service time distribution• A continuous quay operation results in a higher annual throughput or less required quay length
23Modeling arrival process
Thank you!
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